Method of extracting a time constant from complex random telegraph signals

Abstract

A method and apparatus for extracting a time constant from a time series of values of a signal that varies in accordance with multiple charge carrier trap defects that cause Random Telegraph Noise (RTN), using transition-based assignment of states.

What is claimed is: 
     
       1. A characteristic physical constant extraction method comprising:
 receiving a signal representing a change in a drain current of a semiconductor device over time, said signal comprising a time series of values; 
 constructing a histogram representation of said signal by binning each said value; 
 determining a plurality of peaks of said histogram representation, each said peak being associated with a state of a Random Telegraph Noise (RTN) signal caused by a plurality of bistable traps of mobile charge carriers in said semiconductor device; 
 assigning a peak index value for each said peak; 
 calculating an amplitude and a time constant ratio for each said trap; 
 determining theoretical intensities for each said peak; and 
 determining a number of said traps based on a correspondence between the calculated amplitude and time constant ratio for each said trap and said theoretical intensity for each peak associated with each said trap. 
 
     
     
       2. The method of  claim 1 , wherein said assigning a peak index value comprises:
 (a) assigning a lowest peak index value to one of said states in which all said traps are in an empty condition, wherein each said state is comprised of a first state value indicating the empty trap condition and a second state value indicating the capture condition, wherein a transition from said first state value to said second state value represents capture of an electron by an associated trap, and a transition from said second state value to said first state value represents release of an electron from the associated trap, and wherein the drain current of said semiconductor device changes between at least two stable states in response to said transitions; 
 (b) assigning the first state value indicating the empty condition to a lowest peak other than the lowest peak associated with step (a) or the next lowest peak with respect thereto; 
 (c) determining a peak which is nearest in time to a time position in which the peak value is the lowest peak in step (b) plus an offset value; 
 (d) assigning the second state value indicating the capture condition to the peak determined in step (c); 
 (e) repeating steps (b) through (d) for all peaks in said time series; 
 (f) classifying all peaks in said time series into one of a first set consisting of peaks assigned the first state value indicating the empty condition and a second set consisting of peaks assigned the second state value indicating the capture condition; 
 (g) recursively applying steps (a) through (f) to one of the first set and the second set. 
 
     
     
       3. The method of  claim 2 , wherein said determining a peak at step (c) comprises:
 for each said trap, calculating a difference in position between corresponding peaks in said first set and said second set to determine said amplitude; 
 calculating a first sum based on intensities of the peaks of said first set; 
 calculating a second sum based on intensities of the peaks of said second set; and 
 for each said trap, calculating a ratio of said first and second sums to determine said time constant ratio. 
 
     
     
       4. The method of  claim 2 , wherein said assigning a peak index value further comprises:
 creating a look-up table defining a number of allowed next-state transitions from each said state, wherein each said allowed next-state transition is a transition to a state that differs from a current state by 1 binary digit; and 
 wherein said allowed next-state transitions exclude transitions to any state other than one of said allowed next-state transitions, to prevent state assignment errors caused by Gaussian noise during said assigning a peak index value. 
 
     
     
       5. The method of  claim 1 , wherein said assigning a peak index value comprises:
 (a) assigning a highest peak index value to one of said states in which all said traps are in a capture condition, wherein each said state is comprised of a first state value indicating the empty trap condition and a second state value indicating the capture condition, wherein a transition from said first state value to said second state value represents capture of an electron by an associated trap, and a transition from said second state value to said first state value represents release of an electron from the associated trap, and wherein the drain current of said semiconductor device changes between at least two stable states in response to said transitions; 
 (b) assigning the second state value indicating the capture condition to a highest peak other than the highest peak associated with step (a) or the next highest peak with respect thereto; 
 (c) determining a peak which is nearest in time to a time position in which the peak value is the highest peak in step (b) plus an offset value; 
 (d) assigning the first state value indicating the empty condition to the peak determined in step (c); 
 (e) repeating steps (b) through (d) for all peaks in said time series; 
 (f) classifying all peaks in said time series into one of a first set consisting of peaks assigned the first state value indicating the empty condition and a second set consisting of peaks assigned the second state value indicating the capture condition; 
 (g) recursively applying steps (a) through (f) to one of the first set and the second set. 
 
     
     
       6. The method of  claim 5 , wherein said determining a peak at step (c) comprises:
 for each said trap, calculating a difference in position between corresponding peaks in said first set and said second set to determine said amplitude; 
 calculating a first sum based on intensities of the peaks of said first set; 
 calculating a second sum based on intensities of the peaks of said second set; and 
 for each said trap, calculating a ratio of said first and second sums to determine said time constant ratio. 
 
     
     
       7. The method of  claim 5 , wherein said assigning a peak index value further comprises:
 creating a look-up table defining a number of allowed next-state transitions from each said state, wherein each said allowed next-state transition is a transition to a state that differs from a current state by 1 binary digit; and 
 wherein said allowed next-state transitions exclude transitions to any state other than one of said allowed next-state transitions, to prevent state assignment errors caused by Gaussian noise during said assigning a peak index value. 
 
     
     
       8. A method of extracting characteristic physical constants from a complex Random Telegraph Noise (RTN) signal, the method comprising:
 resolving a number of stable states in a time series, said stable states being associated with a plurality of defects in a semiconductor device, said time series comprising a plurality of data points; 
 determining an activation status of each said defect; 
 calculating a transition preference table based on physically allowed transitions; and 
 uniquely assigning each said data point of said time series to one said stable state using said transition preference table. 
 
     
     
       9. The method of  claim 8 ,
 wherein each said defect comprises a bistable trap of a mobile charge carrier in said semiconductor device, and 
 wherein said plurality of defects causes Random Telegraph Noise (RTN) in a voltage threshold of one or more gates of said semiconductor device. 
 
     
     
       10. The method of  claim 8 , further comprising:
 assigning a peak index value for each of a plurality of peaks of said time series, each said peak associated with one said defect; 
 calculating an amplitude and a time constant ratio for each said defect; 
 determining theoretical intensities for each said peak; and 
 determining a number of said defects based on a correspondence between said calculated amplitude and time constant ratio for each said defect and said theoretical intensity for each peak associated with said defect, 
 wherein said assigning a peak index value for each of a plurality of peaks uses a standard deviation based on physical characteristics of a measuring system. 
 
     
     
       11. The method of  claim 10 , wherein said assigning a peak index value comprises:
 (a) assigning a lowest peak index value to one of said states in which all said traps are in an empty condition, wherein each said state is comprised of a first state value indicating the empty trap condition and a second state value indicating the capture condition, wherein a transition from said first state value to said second state value represents capture of an electron by an associated trap, and a transition from said second state value to said first state value represents release of an electron from the associated trap, and wherein the drain current of said semiconductor device changes between at least two stable states in response to said transitions; 
 (b) assigning the first state value indicating the empty condition to a lowest peak other than the lowest peak associated with step (a) or the next lowest peak with respect thereto; 
 (c) determining a peak which is nearest in time to a time position in which the peak value is the lowest peak in step (b) plus an offset value; 
 (d) assigning the second state value indicating the capture condition to the peak determined in step (c); 
 (e) repeating steps (b) through (d) for all peaks in said time series; 
 (f) classifying all peaks in said time series into one of a first set consisting of peaks assigned the first state value indicating the empty condition and a second set consisting of peaks assigned the second state value indicating the capture condition; 
 (g) recursively applying steps (a) through (f) to one of the first set and the second set. 
 
     
     
       12. The method of  claim 11 , wherein said determining a peak at step (c) comprises:
 for each said trap, calculating a difference in position between corresponding peaks in said first set and said second set to determine said amplitude; 
 calculating a first sum based on intensities of the peaks of said first set; 
 calculating a second sum based on intensities of the peaks of said second set; and 
 for each said trap, calculating a ratio of said first and second sums to determine said time constant ratio. 
 
     
     
       13. The method of  claim 11 , wherein said assigning a peak index value further comprises:
 creating a look-up table defining a number of allowed next-state transitions from each said state, wherein each said allowed next-state transition is a transition to a state that differs from a current state by 1 binary digit; and 
 wherein said allowed next-state transitions exclude transitions to any state other than one of said allowed next-state transitions, to prevent state assignment errors caused by Gaussian noise during said assigning a peak index value. 
 
     
     
       14. The method of  claim 10 , wherein said assigning a peak index value comprises:
 (a) assigning a highest peak index value to one of said states in which all said traps are in a capture condition, wherein each said state is comprised of a first state value indicating the empty trap condition and a second state value indicating the capture condition, wherein a transition from said first state value to said second state value represents capture of an electron by an associated trap, and a transition from said second state value to said first state value represents release of an electron from the associated trap, and wherein the drain current of said semiconductor device changes between at least two stable states in response to said transitions; 
 (b) assigning the second state value indicating the capture condition to a highest peak other than the highest peak associated with step (a) or the next highest peak with respect thereto; 
 (c) determining a peak which is nearest in time to a time position in which the peak value is the highest peak in step (b) plus an offset value; 
 (d) assigning the first state value indicating the empty condition to the peak determined in step (c); 
 (e) repeating steps (b) through (d) for all peaks in said time series; 
 (f) classifying all peaks in said time series into one of a first set consisting of peaks assigned the first state value indicating the empty condition and a second set consisting of peaks assigned the second state value indicating the capture condition; 
 (g) recursively applying steps (a) through (f) to one of the first set and the second set. 
 
     
     
       15. The method of  claim 14 , wherein said determining a peak at step (c) comprises:
 for each said trap, calculating a difference in position between corresponding peaks in said first set and said second set to determine said amplitude; 
 calculating a first sum based on intensities of the peaks of said first set; 
 calculating a second sum based on intensities of the peaks of said second set; and 
 for each said trap, calculating a ratio of said first and second sums to determine said time constant ratio. 
 
     
     
       16. The method of  claim 14 , wherein said assigning a peak index value further comprises:
 creating a look-up table defining a number of allowed next-state transitions from each said state, wherein each said allowed next-state transition is a transition to a state that differs from a current state by 1 binary digit; and 
 wherein said allowed next-state transitions exclude transitions to any state other than one of said allowed next-state transitions, to prevent state assignment errors caused by Gaussian noise during said assigning a peak index value. 
 
     
     
       17. The method of  claim 8 , wherein said uniquely assigning each said data point is performed based on a dynamic threshold that is different from an equilibrium threshold. 
     
     
       18. The method of  claim 8 , wherein the number of said defects is three or more. 
     
     
       19. An apparatus for extracting characteristic physical constants from a complex Random Telegraph Noise (RTN) signal, the apparatus comprising:
 a first stage configured to resolve a number of stable states in a time series, said stable states being associated with a plurality of defects, said time series comprising a plurality of data points, and to determine an activation status of each said defect; and 
 a second stage configured to calculate a transition preference table based on physically allowed transitions, and to uniquely assign each said data point of said time series to one said stable state using said transition preference table, 
 wherein each said defect comprises a bistable trap of a mobile charge carrier in said semiconductor device, and 
 wherein said plurality of defects causes Random Telegraph Noise (RTN) in a voltage threshold of one or more gates of said semiconductor device. 
 
     
     
       20. The apparatus of  claim 19 , wherein said first stage is further configured to:
 assign a peak index value for each of a plurality of peaks of said time series, each said peak being associated with one said defect; 
 calculate an amplitude and a time constant ratio for each said defect; 
 determine a theoretical intensity for each said peak; and 
 determine a number of said defects based on a correspondence between said calculated amplitude and time constant ratio for each said peak and said theoretical intensity for each peak associated with each said defect, 
 wherein said first stage assigns a peak index value for each of a plurality of peaks using a standard deviation based on physical characteristics of a measuring system.